Question

Two masses are connected by a string which passes over a pulley accelerating upward at a rate A shown. If $a_{1}$ and $a_{2}$ be the accelerations of bodies 1 and 2 respectively then,

• A. $A=(a_{1}+a_{2})$
• B. $A=(a_{1}-a_{2})$
• C. $A=\frac{a_{1}-a_{2}}{2}$
• D. $A=\frac{a_{1}+a_{2}}{2}$

Answer 1

Answer: (D)

Since length of the string is constant. So,
$(Y_{p}-y_{1})+\pi R=\left(Y_{p}-y_{2}\right)$ = constant
Take derivative of both sides twice w.r.t. time t,
We get, $\overset{ ..}{Y_{p}}-\overset{¨}{y_{1}}+0+\overset{¨}{Y_{p}}-\overset{¨}{Y_{2}}=0$
$2 \overset{¨}{Y_{p}}=\overset{¨}{y_{1}}+\overset{¨}{y_{2}}$
$\Rightarrow 2A=a_{1}+a_{2}$
$\Rightarrow A=\frac{a_{1}+a_{2}}{2}$